Fly to Oporto, Santiago de Compostela or Vigo. Alvarães is quite close to the town of Viana do Castelo that is 50 km away from Oporto airport (90 km from Vigo and 120 km from Santiago airports). From there you will be in direct link to modern motorways representing 35 minutes, 60 or 90 minutes driving, respectively.
Cheap flights available with Ryanair, AirBerlin and Transavia. You would better to rent a car at the airport with one of the budget car hire companies.